Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds

Understand

In this paper we study the Dirichlet problem for fully nonlinear second-order equations on a riemannian manifold.

• As in a previous paper we define equations via closed subsets of the 2-jet bundle.
• Basic existence and uniqueness theorems are established in a wide variety of settings.
• However, the emphasis is on starting with a constant coefficient equation as a model, which then universally determines an equation on every riemannian manifold which is equipped with a topological reduction of the structure group to the invariance group of the model.